Remember$$Center City Cake Shoppe? They now have a big business serving Philadelphia and its suburbs. They did not change the business model.

The shop still spends $$15$ in making each cake, and has a regular selling price of $$25.$

For every customer facing a stockout, the Cake Shoppe has estimated that there is a goodwill loss of $$5($over and above the lost margin on that sale$).$

Unsold cakes at the end of the day are sold below cost, at $$10,$ and are always sold off before the store closes for the night.$$

Their daily demand distribution is now:

DemandProbability$500\mathrm{.}10600\mathrm{.}15700\mathrm{.}25800\mathrm{.}25900\mathrm{.}151000\mathrm{.}10$

$$

$1.$ The optimal service level for this business is $[$ Select $]["50\%","75\%","90\%","100\%"].$

$2.$ Given this optimal service level, the optimal quantity to hold is $[$ Select $]["70","80","90","100"]$

$3.$ Given this optimal quantity, the expected sales is $[$ Select $]["50","71\mathrm{.}5","75","100"]$ while the expected demand is $[$ Select $]["50","71\mathrm{.}5","75","100"].$

$4.$ The fill rate is $[$ Select $]["75\%","90\%","95\%","100\%"]$ approximately.

$5.$ Center City Cake Shoppe is going to earn the highest profit per day with the above service level, and that profit will be $$[$ Select $]["600","655","675","700"]$